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Examples 3.4.2(b):

What is inf, sup, lim inf and lim sup for ?
Since this sequence is {1, 1/2, 1/3, 1/4, ...} the infimum is zero, while the supremum is 1. As for lim inf and lim sup, we find first the sequence of numbers Aj and Bj mentioned in the definition. and so on. Therefore, it is clear that
lim inf = 0
Similarly, we find the numbers Bj= sup{aj, aj + 1, aj + 2, ...}: and so on. Therefore, it is clear that
lim sup = 0
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